ℓ₁-to-ℓ₁ interval observation design for discrete-time switched linear systems under dwell time constraint

ABSTRACT

In this brief article, sufficient conditions characterising the ${\ell }_1$-gain of discrete-time switched positive linear systems (DSPLSs) under dwell time constraint are obtained. The dwell time refers to range, minimum and constant dwell time. These conditions are presented in terms of linear programming. Then, convex sufficient conditions on the existence of ${\ell }_1$-to-${\ell }_1$ interval observers for discrete-time switched linear systems (DSLSs) are derived based on the ${\ell }_1$-gain stability analysis results of DSPLSs. By adding some parameter matrices, the proposed interval observer has a new structure that relaxes the design conditions. Suitable observer gains can be extracted from the solution of the dimensional optimisation problem where the ${\ell }_1$-gain of the system mapping the disturbances to the weighted observation errors is minimised. At last, some numerical examples of DSLSs are given for illustration.

KEYWORDS:

• Discrete-time switched positive linear systems (DSPLSs)
• discrete-time switched linear systems (DSLSs)
• ${\ell }_1$-to-${\ell }_1$ interval observation
• dwell time
• optimisation

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grants No. 61971100).

Notes on contributors

Xiaozeng Xu

Xiaozeng Xu received the B.S. degree in electronic information science and technology from Shandong university of science and technology, Shandong, China, in 2017. He is currently working toward the Ph.D. degree with the University of Electronic Science and Technology of China, Sichuan, China. His research interests include fuzzy systems and switched systems.

Yang Li

Yang Li received the B.S. degree in electronic and information engineering from University of Electronic Science and Technology of China, Chengdu, in 2014. He is pursuing for the M.S. degree in circuits and systems at the University of Electronic Science and Technology of China, Chengdu. His research interests include intelligent control, switched systems, fuzzy systems.

Can Liu

Can Liu received the B.S. degree in electronic information science and technology from the Jiangsu University of Science and Technology, Jiangsu, China, in 2013. He is currently pursuing the Ph.D. degree with the University of Electronic Science and Technology of China, Sichuan, China. His research interests include fuzzy systems, nonlinear systems, and switched systems.

Hongbin Zhang

Hongbin Zhang received the B.Eng. degree in aerocraft design from Northwestern Polytechnical University, Xi’an, China, in 1999, and the M.Eng. and Ph.D. degrees in circuits and systems from the University of Electronic Science and Technology of China, Chengdu, China, in 2002 and 2006, respectively. He has been with the School of Electrical Engineering, University of Electronic Science and Technology of China, since 2002, where he is currently a Professor. Since December 2011, he has been a Postdoctoral Researcher with the School of Automation, Nanjing University of Science and Technology, Nanjing, China. His current research interests include fuzzy control, stochastic control, and time-delay control systems.